The eigenvalues and eigenvectors of the Hilbert Schmidt operators corresponding to the Wiener functionals of order 2, which give a rise of soliton solutions of the KdV equation, are determined.
We present low-order functional observer existence conditions; the proposed existence conditions always lead to a design of functional observers of order less than or equal to that of a Luenberger observer.
A multi-valued iterative functional equation of order n is considered.
We will refer to (1) in this paper as a classical polynomial functional equation of order n.
These disorder-based functions represent a crucial complementation to the functional repertoire of ordered proteins.
Their functions, which are typically associated with a wide range of intermolecular interactions where IDPs possess remarkable binding promiscuity, complement functional repertoire of ordered proteins.
Several simplified membrane models featuring coexisting liquid disordered (Ld) and ordered (Lo) lipid phases have been developed to mimic the heterogeneous organization of cellular membranes, and thus, aid our understanding of the nature and functional role of ordered lipid protein nanodomains, termed "rafts".
The weighted K-functional of second order for (fin C[0,1]) is defined by K_{2,Phi}(f,delta):= infbigl{ | f-g|+deltabigl| Phi^{2} g^{primeprime}bigr|, gin W^{2}(Phi) bigr},quad deltageq0, where W^{2}(Phi):=bigl{ gin C[0,1]mid g^{prime}in AC[0,1], Phi^{2}g^{primeprime }in C[0,1]bigr} and AC[0,1]:=bigl{ hmid h mbox{ is absolutely continuous in } [a,b], mbox{ for every } 0< a< b< 1bigr}.
While some can be moody and muted in the morning, hopefully by lunchtime the brain has managed to crank itself into some kind of functional order.
These results suggest that similar to interaction with SMN, SIP1 may recognize the dimer form of IN preferentially and play an important role of the stabilization of functional high-order structure forms of IN.
